The disclosure describes various aspects of techniques for cooling a chain of ions to near the combined ground state that does not grow with the number of ions in the chain. By addressing each ion individually and using each ion to cool a different motional mode, it is possible to cool the motional modes concurrently. In an example, a third of the total motional modes can be cooled at the same time. In an aspect, the techniques include generating a sideband cooling laser beam for each ion in the ion chain, concurrently cooling two or more motional modes associated with the ions in the ion chain using the respective sideband cooling laser beam until each of the two or more motional modes reaches a motional ground state, and performing a quantum computation using the ion chain after the two or more motional modes have reached the motional ground state.